Optimization of high-energy-compaction, nearly-orthonormal, linear-phase filter banks

In this paper, we design two-channel, perfect-reconstruction, linear-phase, biorthogonal filter banks that maximize orthonormality subject to structural constraints on the filter bank. These structural constraints may be adjusted so as to provide various degrees of energy compaction. The applications targeted are in compression. Proper cost functions are formulated and an efficient signal-adaptive optimization algorithm is proposed. Our algorithm is motivated by a number of interesting properties of the correlation matrix of typical signals and images, and efficiently uses the degrees of freedom in the parameterization of perfect reconstruction filter banks. The algorithm provides different levels of tradeoff between the energy compaction and approximate orthonormality goals. Comparisons with the popular Daubechies 9-7 filter bank show significant improvements in terms of orthogonality and energy compaction.